Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 1 4.945149
beta0_black 1 1.753339
beta1_pelagic 4 1.612456
beta3_black 1 1.548789
beta0_pelagic 4 1.488203
beta0_pH 3 1.329349
beta3_yellow 1 1.326645
beta2_black 1 1.257899
beta2_pH 7 1.252937
beta3_pelagic 1 1.251454
parameter n badRhat_avg
beta1_pH 14 1.251049
tau_beta0_pH 2 1.250190
beta2_yellow 3 1.230160
tau_beta0_pelagic 1 1.215745
beta1_yellow 4 1.214770
beta3_pH 2 1.171122
beta2_pelagic 3 1.163080
beta0_yellow 1 1.143092
beta4_pelagic 1 1.133608
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside NG NSEI NSEO PWSI PWSO SOKO2SAP SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 0 0 0 0 0
beta0_pelagic 0 0 0 1 0 0 0 0 1 1 0 1 0
beta0_pH 0 1 0 0 0 0 0 0 0 0 1 0 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 0 0 1
beta1_black 0 0 1 0 0 0 0 0 0 0 0 0 0
beta1_pelagic 0 0 0 1 0 0 0 0 1 1 0 1 0
beta1_pH 1 1 0 0 1 1 0 0 1 1 1 0 1
beta1_yellow 0 1 1 0 0 0 0 0 1 0 0 0 1
beta2_black 0 0 1 0 0 0 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 0 0 1 0 1 0 0 0 0
beta2_pH 0 0 1 0 0 1 0 0 1 1 0 0 0
beta2_yellow 0 0 0 1 0 0 1 0 1 0 0 0 0
beta3_black 0 0 1 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 1 0 0 0
beta3_pH 0 0 0 0 0 0 0 0 0 0 0 0 1
beta3_yellow 0 0 0 0 0 0 0 1 0 0 0 0 0
beta4_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 1 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.119 0.076 -0.258 -0.122 0.038
mu_bc_H[2] -0.094 0.047 -0.175 -0.097 0.007
mu_bc_H[3] -0.438 0.070 -0.570 -0.439 -0.296
mu_bc_H[4] -0.989 0.189 -1.360 -0.992 -0.615
mu_bc_H[5] 0.930 0.912 -0.142 0.737 3.329
mu_bc_H[6] -2.139 0.314 -2.740 -2.142 -1.531
mu_bc_H[7] -0.463 0.109 -0.694 -0.458 -0.257
mu_bc_H[8] 0.259 0.372 -0.350 0.221 1.076
mu_bc_H[9] -0.286 0.133 -0.551 -0.286 -0.020
mu_bc_H[10] -0.109 0.070 -0.239 -0.111 0.032
mu_bc_H[11] -0.122 0.039 -0.197 -0.122 -0.047
mu_bc_H[12] -0.255 0.108 -0.488 -0.251 -0.054
mu_bc_H[13] -0.134 0.076 -0.284 -0.135 0.014
mu_bc_H[14] -0.305 0.095 -0.494 -0.304 -0.126
mu_bc_H[15] -0.342 0.050 -0.439 -0.342 -0.237
mu_bc_H[16] -0.263 0.372 -0.909 -0.291 0.567
mu_bc_R[1] 1.339 0.146 1.058 1.338 1.629
mu_bc_R[2] 1.441 0.093 1.256 1.442 1.621
mu_bc_R[3] 1.402 0.142 1.130 1.401 1.678
mu_bc_R[4] 0.892 0.201 0.467 0.901 1.265
mu_bc_R[5] 1.174 0.470 0.241 1.180 2.090
mu_bc_R[6] -1.641 0.404 -2.445 -1.644 -0.853
mu_bc_R[7] 0.320 0.193 -0.062 0.325 0.689
mu_bc_R[8] 0.519 0.192 0.147 0.518 0.883
mu_bc_R[9] 0.298 0.214 -0.163 0.310 0.677
mu_bc_R[10] 1.313 0.157 0.990 1.318 1.608
mu_bc_R[11] 1.036 0.099 0.841 1.039 1.226
mu_bc_R[12] 0.826 0.197 0.436 0.825 1.204
mu_bc_R[13] 1.028 0.101 0.822 1.029 1.223
mu_bc_R[14] 0.895 0.143 0.617 0.898 1.166
mu_bc_R[15] 0.783 0.110 0.567 0.783 1.001
mu_bc_R[16] 1.089 0.125 0.841 1.090 1.329
tau_pH[1] 5.178 0.445 4.356 5.167 6.083
tau_pH[2] 2.007 0.223 1.600 1.994 2.479
tau_pH[3] 2.276 0.227 1.854 2.267 2.738
beta0_pH[1,1] 0.575 0.166 0.237 0.580 0.881
beta0_pH[2,1] 1.389 0.170 1.056 1.391 1.700
beta0_pH[3,1] 1.422 0.180 1.045 1.432 1.753
beta0_pH[4,1] 1.588 0.197 1.174 1.599 1.952
beta0_pH[5,1] -0.891 0.318 -1.612 -0.859 -0.377
beta0_pH[6,1] -0.931 0.664 -2.899 -0.791 -0.092
beta0_pH[7,1] 0.363 0.721 -1.245 0.763 0.990
beta0_pH[8,1] -0.781 0.324 -1.586 -0.743 -0.289
beta0_pH[9,1] -0.699 0.352 -1.492 -0.664 -0.145
beta0_pH[10,1] 0.475 0.165 0.154 0.480 0.786
beta0_pH[11,1] -0.066 0.172 -0.423 -0.060 0.252
beta0_pH[12,1] 0.499 0.182 0.144 0.503 0.852
beta0_pH[13,1] 0.007 0.147 -0.287 0.011 0.290
beta0_pH[14,1] -0.320 0.167 -0.664 -0.318 0.000
beta0_pH[15,1] -0.013 0.179 -0.389 -0.006 0.324
beta0_pH[16,1] -0.512 0.376 -1.367 -0.440 0.048
beta0_pH[1,2] 2.797 0.181 2.439 2.798 3.150
beta0_pH[2,2] 2.890 0.147 2.596 2.892 3.172
beta0_pH[3,2] 3.137 0.243 2.386 3.165 3.482
beta0_pH[4,2] 2.955 0.150 2.665 2.957 3.231
beta0_pH[5,2] 4.988 1.635 2.936 4.585 9.290
beta0_pH[6,2] 3.125 0.215 2.707 3.127 3.541
beta0_pH[7,2] 1.958 0.174 1.621 1.953 2.303
beta0_pH[8,2] 2.867 0.180 2.513 2.867 3.206
beta0_pH[9,2] 3.438 0.237 2.962 3.438 3.884
beta0_pH[10,2] 3.621 0.219 3.182 3.617 4.043
beta0_pH[11,2] -4.841 0.309 -5.475 -4.832 -4.254
beta0_pH[12,2] -4.774 0.391 -5.563 -4.769 -3.988
beta0_pH[13,2] -4.563 0.407 -5.337 -4.573 -3.727
beta0_pH[14,2] -5.609 0.473 -6.604 -5.598 -4.763
beta0_pH[15,2] -4.267 0.341 -4.899 -4.267 -3.592
beta0_pH[16,2] -4.865 0.394 -5.674 -4.852 -4.130
beta0_pH[1,3] 0.686 0.537 -0.597 0.802 1.422
beta0_pH[2,3] 2.118 0.250 1.485 2.154 2.472
beta0_pH[3,3] 2.341 0.333 1.518 2.424 2.779
beta0_pH[4,3] 2.875 0.300 2.031 2.921 3.242
beta0_pH[5,3] 2.573 2.301 -1.059 2.433 7.694
beta0_pH[6,3] 0.170 1.068 -1.824 0.298 1.816
beta0_pH[7,3] -1.940 0.762 -3.097 -2.021 0.473
beta0_pH[8,3] 0.328 0.198 -0.049 0.324 0.734
beta0_pH[9,3] -0.584 0.466 -1.953 -0.511 0.032
beta0_pH[10,3] 0.013 1.038 -2.321 0.340 1.353
beta0_pH[11,3] -0.168 0.337 -0.804 -0.181 0.519
beta0_pH[12,3] -0.869 0.346 -1.594 -0.852 -0.266
beta0_pH[13,3] -0.144 0.314 -0.737 -0.150 0.468
beta0_pH[14,3] -0.290 0.260 -0.779 -0.294 0.230
beta0_pH[15,3] -0.721 0.294 -1.354 -0.714 -0.184
beta0_pH[16,3] -0.403 0.279 -0.944 -0.408 0.154
beta1_pH[1,1] 2.981 0.301 2.428 2.965 3.622
beta1_pH[2,1] 2.131 0.254 1.670 2.121 2.656
beta1_pH[3,1] 1.993 0.277 1.510 1.978 2.590
beta1_pH[4,1] 2.341 0.320 1.819 2.314 2.989
beta1_pH[5,1] 2.320 0.423 1.692 2.265 3.381
beta1_pH[6,1] 4.472 1.441 2.468 4.186 8.205
beta1_pH[7,1] 4.081 4.232 0.260 2.909 17.572
beta1_pH[8,1] 4.466 1.109 2.856 4.257 7.075
beta1_pH[9,1] 2.396 0.502 1.646 2.320 3.628
beta1_pH[10,1] 2.047 0.222 1.632 2.045 2.493
beta1_pH[11,1] 3.242 0.212 2.837 3.238 3.668
beta1_pH[12,1] 2.539 0.216 2.114 2.538 2.958
beta1_pH[13,1] 2.968 0.212 2.566 2.964 3.401
beta1_pH[14,1] 3.426 0.218 3.030 3.415 3.867
beta1_pH[15,1] 2.515 0.224 2.092 2.509 2.965
beta1_pH[16,1] 4.188 0.680 3.202 4.070 5.729
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.003 0.052 0.000 0.000 0.009
beta1_pH[3,2] 0.069 0.282 0.000 0.000 1.192
beta1_pH[4,2] 0.023 0.272 0.000 0.000 0.031
beta1_pH[5,2] 0.001 0.004 0.000 0.000 0.014
beta1_pH[6,2] 0.018 0.217 0.000 0.000 0.019
beta1_pH[7,2] 0.002 0.020 0.000 0.000 0.007
beta1_pH[8,2] 0.004 0.050 0.000 0.000 0.008
beta1_pH[9,2] 0.007 0.087 0.000 0.000 0.012
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.676 0.341 6.030 6.661 7.393
beta1_pH[12,2] 6.446 0.465 5.579 6.429 7.418
beta1_pH[13,2] 6.949 0.448 6.081 6.952 7.853
beta1_pH[14,2] 7.241 0.490 6.355 7.230 8.275
beta1_pH[15,2] 6.750 0.383 5.963 6.754 7.465
beta1_pH[16,2] 7.455 0.429 6.642 7.443 8.323
beta1_pH[1,3] 2.727 1.122 1.374 2.440 5.680
beta1_pH[2,3] 2.542 10.743 0.000 0.025 36.638
beta1_pH[3,3] 0.337 0.629 0.000 0.030 1.548
beta1_pH[4,3] 1.038 6.346 0.000 0.016 4.975
beta1_pH[5,3] 2.800 13.260 0.000 2.141 8.214
beta1_pH[6,3] 1.578 1.520 0.000 1.703 3.774
beta1_pH[7,3] 2.778 0.794 0.068 2.863 3.992
beta1_pH[8,3] 2.634 0.403 1.844 2.662 3.325
beta1_pH[9,3] 2.628 0.502 1.862 2.579 3.852
beta1_pH[10,3] 3.417 1.173 1.813 3.114 6.096
beta1_pH[11,3] 2.753 0.386 2.017 2.750 3.504
beta1_pH[12,3] 4.129 0.429 3.316 4.126 5.007
beta1_pH[13,3] 1.729 0.337 1.057 1.730 2.366
beta1_pH[14,3] 2.553 0.339 1.894 2.554 3.236
beta1_pH[15,3] 2.001 0.315 1.409 2.000 2.647
beta1_pH[16,3] 1.816 0.308 1.215 1.816 2.429
beta2_pH[1,1] 0.503 0.125 0.314 0.485 0.797
beta2_pH[2,1] 0.559 0.217 0.263 0.528 1.093
beta2_pH[3,1] 0.603 0.286 0.253 0.554 1.239
beta2_pH[4,1] 0.502 0.201 0.238 0.474 0.932
beta2_pH[5,1] 1.827 1.372 0.206 1.635 5.251
beta2_pH[6,1] 0.157 0.062 0.066 0.147 0.308
beta2_pH[7,1] -1.479 1.892 -6.201 -1.216 0.847
beta2_pH[8,1] 0.209 0.070 0.111 0.197 0.377
beta2_pH[9,1] 0.435 0.270 0.147 0.386 0.990
beta2_pH[10,1] 0.616 0.207 0.341 0.582 1.105
beta2_pH[11,1] 0.799 0.218 0.488 0.763 1.334
beta2_pH[12,1] 1.362 0.508 0.746 1.258 2.485
beta2_pH[13,1] 0.747 0.225 0.428 0.713 1.265
beta2_pH[14,1] 0.834 0.209 0.529 0.802 1.346
beta2_pH[15,1] 0.809 0.274 0.419 0.762 1.477
beta2_pH[16,1] 0.364 0.167 0.168 0.317 0.815
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 1.421 10.588 -19.920 1.264 20.873
beta2_pH[3,2] 1.424 10.595 -19.649 0.997 21.433
beta2_pH[4,2] 1.549 10.604 -19.610 1.344 20.414
beta2_pH[5,2] -0.373 10.631 -20.796 -0.404 20.232
beta2_pH[6,2] -0.425 10.577 -20.269 -0.447 20.249
beta2_pH[7,2] -0.356 10.570 -20.381 -0.473 20.331
beta2_pH[8,2] -0.470 10.599 -20.611 -0.242 20.480
beta2_pH[9,2] -0.458 10.530 -20.407 -0.404 20.141
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.335 3.591 -17.903 -8.749 -4.225
beta2_pH[12,2] -7.176 4.441 -17.674 -6.782 -0.873
beta2_pH[13,2] -6.993 4.301 -17.467 -6.337 -1.531
beta2_pH[14,2] -7.851 3.941 -17.170 -7.220 -2.474
beta2_pH[15,2] -8.779 3.559 -18.224 -8.177 -3.869
beta2_pH[16,2] -9.184 3.782 -18.685 -8.488 -4.021
beta2_pH[1,3] 2.383 3.346 0.135 0.633 11.393
beta2_pH[2,3] 0.394 5.098 -6.864 0.330 12.194
beta2_pH[3,3] 0.678 5.082 -8.277 0.053 12.567
beta2_pH[4,3] 1.300 4.912 -7.649 0.686 12.631
beta2_pH[5,3] 10.462 6.416 0.590 9.631 24.653
beta2_pH[6,3] 10.348 6.462 0.260 9.405 24.743
beta2_pH[7,3] 10.212 6.376 1.054 9.278 24.587
beta2_pH[8,3] 11.096 5.791 2.467 10.232 24.450
beta2_pH[9,3] 10.272 6.371 0.442 9.422 24.113
beta2_pH[10,3] 2.662 3.442 0.284 0.966 12.255
beta2_pH[11,3] -2.220 2.009 -8.204 -1.683 -0.590
beta2_pH[12,3] -2.339 1.879 -8.556 -1.813 -0.940
beta2_pH[13,3] -2.834 2.365 -9.826 -2.103 -0.810
beta2_pH[14,3] -2.717 2.169 -9.331 -2.076 -0.913
beta2_pH[15,3] -2.910 2.273 -9.218 -2.160 -1.010
beta2_pH[16,3] -2.977 2.360 -9.922 -2.195 -0.911
beta3_pH[1,1] 35.765 0.822 34.180 35.770 37.406
beta3_pH[2,1] 33.637 1.135 31.635 33.556 36.184
beta3_pH[3,1] 33.731 1.022 31.803 33.694 35.787
beta3_pH[4,1] 33.783 1.120 31.739 33.723 36.080
beta3_pH[5,1] 27.666 1.137 26.359 27.456 30.833
beta3_pH[6,1] 38.966 3.622 31.633 38.917 45.412
beta3_pH[7,1] 24.322 7.687 18.241 20.622 44.446
beta3_pH[8,1] 40.520 2.305 36.402 40.352 45.321
beta3_pH[9,1] 30.546 1.489 27.795 30.467 33.764
beta3_pH[10,1] 33.116 0.937 31.352 33.097 35.036
beta3_pH[11,1] 30.350 0.476 29.432 30.341 31.305
beta3_pH[12,1] 30.184 0.394 29.393 30.195 30.940
beta3_pH[13,1] 33.195 0.594 32.100 33.186 34.413
beta3_pH[14,1] 32.038 0.453 31.193 32.022 32.930
beta3_pH[15,1] 31.226 0.645 29.939 31.239 32.449
beta3_pH[16,1] 32.098 1.092 30.270 31.942 34.636
beta3_pH[1,2] 30.016 7.961 18.465 28.975 44.934
beta3_pH[2,2] 29.842 7.910 18.518 28.829 45.028
beta3_pH[3,2] 30.611 8.287 18.501 29.655 44.873
beta3_pH[4,2] 30.048 8.075 18.476 28.970 44.847
beta3_pH[5,2] 29.593 7.997 18.372 28.455 44.910
beta3_pH[6,2] 30.080 7.888 18.476 29.358 44.831
beta3_pH[7,2] 29.759 7.866 18.500 28.961 44.546
beta3_pH[8,2] 29.988 7.860 18.522 29.167 44.776
beta3_pH[9,2] 29.776 7.919 18.489 28.642 44.888
beta3_pH[10,2] 29.738 7.955 18.500 28.771 44.895
beta3_pH[11,2] 43.402 0.181 43.123 43.378 43.782
beta3_pH[12,2] 43.187 0.195 42.856 43.143 43.692
beta3_pH[13,2] 43.855 0.154 43.443 43.897 44.054
beta3_pH[14,2] 43.307 0.200 43.049 43.260 43.808
beta3_pH[15,2] 43.404 0.190 43.109 43.379 43.801
beta3_pH[16,2] 43.498 0.186 43.166 43.497 43.840
beta3_pH[1,3] 38.927 2.222 34.232 39.471 43.090
beta3_pH[2,3] 29.592 7.906 18.428 28.428 44.703
beta3_pH[3,3] 32.315 8.675 18.627 32.385 44.814
beta3_pH[4,3] 29.471 7.944 18.367 28.066 44.957
beta3_pH[5,3] 28.263 7.399 18.401 26.674 43.828
beta3_pH[6,3] 28.712 7.042 18.809 26.131 44.681
beta3_pH[7,3] 26.750 1.920 25.027 26.435 29.738
beta3_pH[8,3] 41.484 0.249 41.057 41.489 41.907
beta3_pH[9,3] 33.274 1.279 28.417 33.540 34.225
beta3_pH[10,3] 34.991 1.524 31.595 35.494 36.929
beta3_pH[11,3] 41.789 0.811 40.138 41.822 43.301
beta3_pH[12,3] 41.724 0.377 40.963 41.736 42.468
beta3_pH[13,3] 42.759 0.861 41.126 42.765 44.692
beta3_pH[14,3] 41.114 0.556 39.920 41.132 42.142
beta3_pH[15,3] 42.641 0.632 41.287 42.711 43.696
beta3_pH[16,3] 42.886 0.716 41.238 42.982 44.046
beta0_pelagic[1] 2.211 0.130 1.964 2.214 2.468
beta0_pelagic[2] 1.515 0.120 1.279 1.513 1.749
beta0_pelagic[3] 0.333 0.483 -0.889 0.376 0.945
beta0_pelagic[4] 0.313 0.551 -1.064 0.349 1.154
beta0_pelagic[5] 1.174 0.248 0.664 1.178 1.648
beta0_pelagic[6] 1.475 0.275 0.878 1.503 1.961
beta0_pelagic[7] 1.646 0.220 1.265 1.635 2.123
beta0_pelagic[8] 1.761 0.208 1.366 1.759 2.197
beta0_pelagic[9] 2.474 0.321 1.858 2.475 3.052
beta0_pelagic[10] 2.495 0.208 2.055 2.501 2.889
beta0_pelagic[11] 0.142 0.495 -1.123 0.281 0.712
beta0_pelagic[12] 1.689 0.142 1.418 1.688 1.974
beta0_pelagic[13] 0.319 0.194 -0.081 0.330 0.674
beta0_pelagic[14] -0.124 0.287 -0.767 -0.098 0.355
beta0_pelagic[15] -0.264 0.137 -0.531 -0.263 0.005
beta0_pelagic[16] 0.204 0.386 -0.779 0.325 0.666
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 0.653 0.636 0.000 0.668 2.122
beta1_pelagic[4] 0.849 0.616 0.000 0.842 2.328
beta1_pelagic[5] -0.075 0.316 -0.720 -0.082 0.550
beta1_pelagic[6] -0.116 0.473 -0.881 -0.189 0.787
beta1_pelagic[7] -0.025 0.316 -0.647 -0.024 0.597
beta1_pelagic[8] 0.000 0.279 -0.542 0.004 0.580
beta1_pelagic[9] 0.225 0.498 -0.760 0.357 0.973
beta1_pelagic[10] 0.065 0.278 -0.474 0.067 0.610
beta1_pelagic[11] 3.448 1.108 2.117 3.130 6.147
beta1_pelagic[12] 2.789 0.294 2.242 2.782 3.389
beta1_pelagic[13] 2.897 0.759 1.767 2.761 4.670
beta1_pelagic[14] 4.471 1.078 2.820 4.318 6.756
beta1_pelagic[15] 2.930 0.254 2.426 2.924 3.441
beta1_pelagic[16] 3.916 1.264 2.691 3.366 7.134
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 1.787 3.254 -5.306 1.236 9.097
beta2_pelagic[4] 2.083 3.081 -4.764 1.531 8.952
beta2_pelagic[5] -0.010 0.667 -1.395 -0.009 1.361
beta2_pelagic[6] -0.135 0.692 -1.539 -0.182 1.281
beta2_pelagic[7] -0.003 0.653 -1.318 -0.001 1.372
beta2_pelagic[8] -0.009 0.652 -1.402 -0.013 1.407
beta2_pelagic[9] 0.205 0.679 -1.250 0.264 1.515
beta2_pelagic[10] 0.039 0.638 -1.296 0.033 1.442
beta2_pelagic[11] 2.760 4.741 0.109 0.364 16.941
beta2_pelagic[12] 6.314 5.277 1.147 4.691 21.035
beta2_pelagic[13] 1.013 2.348 0.203 0.469 6.297
beta2_pelagic[14] 0.312 0.149 0.152 0.278 0.685
beta2_pelagic[15] 6.348 5.027 1.301 4.948 20.842
beta2_pelagic[16] 4.663 5.771 0.155 2.794 20.369
beta3_pelagic[1] 29.826 7.881 18.487 28.751 44.993
beta3_pelagic[2] 29.768 7.988 18.525 28.501 44.822
beta3_pelagic[3] 29.455 5.697 19.005 29.483 43.081
beta3_pelagic[4] 26.193 4.637 19.707 25.540 41.125
beta3_pelagic[5] 30.205 8.191 18.483 28.743 45.229
beta3_pelagic[6] 31.860 6.680 18.919 31.749 44.129
beta3_pelagic[7] 29.504 7.594 18.489 28.603 44.815
beta3_pelagic[8] 29.460 8.053 18.446 27.888 44.895
beta3_pelagic[9] 30.739 6.005 19.059 30.691 42.744
beta3_pelagic[10] 29.198 7.943 18.350 27.756 44.843
beta3_pelagic[11] 42.494 1.815 38.061 43.042 45.214
beta3_pelagic[12] 43.452 0.258 43.007 43.441 43.929
beta3_pelagic[13] 42.780 1.332 40.289 42.723 45.556
beta3_pelagic[14] 42.496 1.685 39.101 42.503 45.631
beta3_pelagic[15] 43.170 0.255 42.565 43.172 43.654
beta3_pelagic[16] 43.211 0.923 40.954 43.234 45.408
mu_beta0_pelagic[1] 1.026 0.832 -0.722 1.081 2.629
mu_beta0_pelagic[2] 1.823 0.379 1.015 1.827 2.538
mu_beta0_pelagic[3] 0.317 0.493 -0.691 0.335 1.291
tau_beta0_pelagic[1] 0.965 1.160 0.062 0.584 4.205
tau_beta0_pelagic[2] 2.924 3.558 0.261 2.059 10.272
tau_beta0_pelagic[3] 1.522 1.187 0.169 1.209 4.605
beta0_yellow[1] -0.534 0.193 -0.971 -0.518 -0.219
beta0_yellow[2] 0.503 0.154 0.181 0.508 0.786
beta0_yellow[3] -0.310 0.184 -0.680 -0.306 0.034
beta0_yellow[4] 0.822 0.290 0.047 0.874 1.205
beta0_yellow[5] -1.224 0.424 -2.089 -1.214 -0.423
beta0_yellow[6] 0.270 0.217 -0.142 0.270 0.704
beta0_yellow[7] 0.902 0.557 -1.066 1.031 1.344
beta0_yellow[8] 0.717 0.626 -1.100 0.941 1.281
beta0_yellow[9] -0.159 0.292 -0.751 -0.151 0.371
beta0_yellow[10] 0.229 0.154 -0.070 0.232 0.521
beta0_yellow[11] -1.954 0.461 -2.871 -1.936 -1.052
beta0_yellow[12] -3.665 0.420 -4.516 -3.640 -2.904
beta0_yellow[13] -3.742 0.479 -4.784 -3.714 -2.926
beta0_yellow[14] -2.101 0.586 -3.094 -2.152 -0.319
beta0_yellow[15] -2.877 0.426 -3.711 -2.874 -2.089
beta0_yellow[16] -2.420 0.447 -3.273 -2.428 -1.510
beta1_yellow[1] 0.687 2.518 0.000 0.415 2.350
beta1_yellow[2] 1.067 0.340 0.599 1.026 1.792
beta1_yellow[3] 0.684 0.420 0.066 0.677 1.249
beta1_yellow[4] 1.428 0.807 0.647 1.201 4.047
beta1_yellow[5] 3.317 9.106 1.407 2.798 5.573
beta1_yellow[6] 2.285 0.354 1.580 2.285 2.977
beta1_yellow[7] 5.406 8.118 0.702 3.250 29.530
beta1_yellow[8] 2.625 4.764 0.037 1.859 10.433
beta1_yellow[9] 1.661 0.459 0.889 1.634 2.667
beta1_yellow[10] 2.430 0.454 1.635 2.413 3.371
beta1_yellow[11] 2.100 0.449 1.189 2.102 3.003
beta1_yellow[12] 2.467 0.439 1.655 2.445 3.388
beta1_yellow[13] 2.864 0.483 2.048 2.834 3.912
beta1_yellow[14] 2.210 0.511 1.155 2.223 3.231
beta1_yellow[15] 2.123 0.422 1.331 2.123 2.972
beta1_yellow[16] 2.176 0.445 1.270 2.182 2.999
beta2_yellow[1] -2.682 2.792 -9.310 -2.136 1.786
beta2_yellow[2] -2.990 2.313 -8.225 -2.349 -0.238
beta2_yellow[3] -2.362 2.306 -8.783 -1.492 -0.159
beta2_yellow[4] -2.503 2.631 -9.399 -1.636 -0.086
beta2_yellow[5] -4.354 2.849 -11.049 -3.824 -0.612
beta2_yellow[6] 3.530 2.222 0.934 2.966 9.330
beta2_yellow[7] -4.174 3.611 -11.642 -4.003 4.337
beta2_yellow[8] -2.420 3.994 -10.311 -2.228 5.902
beta2_yellow[9] 3.777 2.859 0.213 3.164 11.684
beta2_yellow[10] -4.325 2.638 -11.047 -3.822 -0.755
beta2_yellow[11] -4.514 2.259 -9.797 -4.016 -1.395
beta2_yellow[12] -4.477 2.261 -10.109 -3.978 -1.451
beta2_yellow[13] -4.291 2.083 -9.877 -3.810 -1.687
beta2_yellow[14] -4.423 2.454 -10.273 -3.898 -0.913
beta2_yellow[15] -3.994 2.181 -9.612 -3.474 -1.150
beta2_yellow[16] -4.503 2.244 -10.043 -4.058 -1.514
beta3_yellow[1] 27.001 7.556 18.330 23.914 44.278
beta3_yellow[2] 29.117 1.813 25.475 28.900 32.958
beta3_yellow[3] 32.881 3.337 24.196 32.889 40.049
beta3_yellow[4] 28.977 3.519 21.470 28.069 35.886
beta3_yellow[5] 33.363 1.553 30.652 33.407 35.780
beta3_yellow[6] 39.678 0.550 38.716 39.632 40.910
beta3_yellow[7] 20.787 3.037 18.538 20.088 29.389
beta3_yellow[8] 25.025 5.648 18.328 24.062 42.163
beta3_yellow[9] 37.804 1.676 35.997 37.591 42.793
beta3_yellow[10] 29.318 0.557 27.943 29.389 30.063
beta3_yellow[11] 45.302 0.537 44.009 45.390 45.979
beta3_yellow[12] 43.310 0.394 42.514 43.283 44.098
beta3_yellow[13] 44.848 0.378 44.020 44.916 45.474
beta3_yellow[14] 43.851 2.640 31.690 44.254 45.817
beta3_yellow[15] 45.184 0.530 44.151 45.183 45.972
beta3_yellow[16] 44.576 0.623 43.418 44.582 45.780
mu_beta0_yellow[1] 0.097 0.563 -1.063 0.105 1.229
mu_beta0_yellow[2] 0.117 0.489 -0.920 0.134 1.061
mu_beta0_yellow[3] -2.453 0.652 -3.444 -2.553 -0.764
tau_beta0_yellow[1] 1.876 2.612 0.089 1.170 7.873
tau_beta0_yellow[2] 1.315 1.221 0.154 0.976 4.359
tau_beta0_yellow[3] 1.508 2.497 0.094 0.899 6.586
beta0_black[1] 0.088 0.190 -0.310 0.106 0.409
beta0_black[2] 1.917 0.129 1.671 1.914 2.174
beta0_black[3] 1.320 0.130 1.061 1.320 1.571
beta0_black[4] 2.423 0.130 2.176 2.421 2.677
beta0_black[5] 1.556 1.982 -3.403 1.667 5.525
beta0_black[6] 1.562 2.012 -3.093 1.673 5.445
beta0_black[7] 1.611 1.999 -2.820 1.667 5.657
beta0_black[8] 1.286 0.223 0.849 1.286 1.723
beta0_black[9] 2.450 0.250 1.978 2.448 2.948
beta0_black[10] 1.472 0.131 1.219 1.474 1.725
beta0_black[11] 3.484 0.148 3.195 3.483 3.770
beta0_black[12] 4.850 0.173 4.499 4.851 5.185
beta0_black[13] -0.104 0.228 -0.566 -0.100 0.323
beta0_black[14] 2.850 0.154 2.541 2.852 3.154
beta0_black[15] 1.290 0.156 0.986 1.289 1.590
beta0_black[16] 4.269 0.158 3.950 4.274 4.569
beta2_black[1] 1.478 3.353 -5.358 1.605 8.145
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.095 1.699 -7.017 -1.553 -0.470
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 34.775 8.422 18.735 38.671 44.617
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.253 0.779 37.564 39.348 40.528
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.272 0.190 -0.650 -0.270 0.101
beta4_black[2] 0.238 0.178 -0.103 0.234 0.588
beta4_black[3] -0.938 0.188 -1.307 -0.933 -0.571
beta4_black[4] 0.424 0.213 -0.002 0.426 0.838
beta4_black[5] 0.174 2.392 -4.875 0.152 4.968
beta4_black[6] 0.211 2.412 -4.323 0.152 5.232
beta4_black[7] 0.229 2.331 -4.417 0.133 5.243
beta4_black[8] -0.689 0.366 -1.400 -0.691 -0.006
beta4_black[9] 1.443 0.995 -0.095 1.331 3.666
beta4_black[10] 0.018 0.188 -0.332 0.017 0.380
beta4_black[11] -0.699 0.211 -1.110 -0.699 -0.291
beta4_black[12] 0.162 0.322 -0.437 0.155 0.792
beta4_black[13] -1.185 0.215 -1.605 -1.179 -0.781
beta4_black[14] -0.184 0.232 -0.646 -0.190 0.254
beta4_black[15] -0.885 0.211 -1.297 -0.883 -0.471
beta4_black[16] -0.598 0.224 -1.027 -0.600 -0.152
mu_beta0_black[1] 1.317 0.890 -0.620 1.356 3.010
mu_beta0_black[2] 1.599 0.877 -0.479 1.652 3.236
mu_beta0_black[3] 2.472 0.999 0.305 2.544 4.314
tau_beta0_black[1] 0.722 0.702 0.058 0.496 2.628
tau_beta0_black[2] 1.901 3.346 0.054 0.847 10.243
tau_beta0_black[3] 0.242 0.166 0.050 0.200 0.668
beta0_dsr[11] -2.905 0.280 -3.451 -2.902 -2.367
beta0_dsr[12] 4.535 0.293 3.994 4.539 5.077
beta0_dsr[13] -1.368 0.363 -2.087 -1.344 -0.779
beta0_dsr[14] -3.651 0.494 -4.618 -3.649 -2.674
beta0_dsr[15] -1.928 0.277 -2.473 -1.926 -1.378
beta0_dsr[16] -2.994 0.360 -3.709 -2.990 -2.338
beta1_dsr[11] 4.840 0.292 4.275 4.842 5.426
beta1_dsr[12] 52.187 352.351 2.334 5.158 51.926
beta1_dsr[13] 2.888 0.442 2.288 2.845 3.737
beta1_dsr[14] 6.317 0.524 5.280 6.319 7.343
beta1_dsr[15] 3.322 0.280 2.785 3.320 3.887
beta1_dsr[16] 5.811 0.375 5.092 5.803 6.557
beta2_dsr[11] -8.357 2.304 -13.963 -8.042 -4.778
beta2_dsr[12] -7.160 2.609 -12.946 -6.979 -2.423
beta2_dsr[13] -6.407 2.791 -12.259 -6.360 -0.697
beta2_dsr[14] -6.305 2.581 -11.611 -6.378 -1.932
beta2_dsr[15] -7.828 2.375 -13.330 -7.559 -3.947
beta2_dsr[16] -8.008 2.279 -13.349 -7.744 -4.399
beta3_dsr[11] 43.487 0.149 43.213 43.481 43.769
beta3_dsr[12] 33.980 0.735 32.146 34.124 34.799
beta3_dsr[13] 43.255 0.341 42.806 43.189 43.884
beta3_dsr[14] 43.335 0.229 43.074 43.263 43.918
beta3_dsr[15] 43.510 0.187 43.162 43.509 43.856
beta3_dsr[16] 43.437 0.157 43.173 43.425 43.756
beta4_dsr[11] 0.582 0.209 0.176 0.574 0.996
beta4_dsr[12] 0.251 0.438 -0.639 0.257 1.126
beta4_dsr[13] -0.171 0.212 -0.605 -0.174 0.238
beta4_dsr[14] 0.147 0.247 -0.346 0.146 0.629
beta4_dsr[15] 0.724 0.212 0.309 0.722 1.154
beta4_dsr[16] 0.145 0.225 -0.297 0.139 0.595
beta0_slope[11] -1.942 0.160 -2.255 -1.938 -1.628
beta0_slope[12] -4.678 0.267 -5.213 -4.673 -4.163
beta0_slope[13] -1.346 0.211 -1.825 -1.325 -0.996
beta0_slope[14] -2.644 0.184 -3.009 -2.643 -2.285
beta0_slope[15] -1.372 0.166 -1.692 -1.370 -1.063
beta0_slope[16] -2.719 0.175 -3.066 -2.721 -2.374
beta1_slope[11] 4.604 0.294 4.041 4.603 5.197
beta1_slope[12] 5.021 0.541 3.977 5.010 6.075
beta1_slope[13] 2.946 0.568 2.229 2.862 4.720
beta1_slope[14] 6.539 0.559 5.515 6.521 7.701
beta1_slope[15] 3.053 0.280 2.494 3.050 3.596
beta1_slope[16] 5.374 0.400 4.616 5.361 6.151
beta2_slope[11] 8.167 2.606 4.420 7.690 15.435
beta2_slope[12] 7.114 2.546 2.785 6.853 12.989
beta2_slope[13] 5.631 3.000 0.370 5.733 11.842
beta2_slope[14] 6.526 2.508 2.323 6.337 12.117
beta2_slope[15] 7.559 2.518 3.589 7.249 13.473
beta2_slope[16] 7.669 2.392 3.975 7.316 13.166
beta3_slope[11] 43.473 0.154 43.196 43.466 43.772
beta3_slope[12] 43.407 0.221 43.068 43.379 43.857
beta3_slope[13] 43.634 0.455 42.934 43.683 44.477
beta3_slope[14] 43.317 0.171 43.090 43.275 43.758
beta3_slope[15] 43.513 0.193 43.156 43.512 43.869
beta3_slope[16] 43.459 0.172 43.160 43.449 43.804
beta4_slope[11] -0.573 0.216 -0.987 -0.575 -0.141
beta4_slope[12] -1.397 0.660 -2.911 -1.317 -0.329
beta4_slope[13] 0.053 0.219 -0.387 0.056 0.472
beta4_slope[14] -0.179 0.262 -0.677 -0.185 0.350
beta4_slope[15] -0.726 0.211 -1.167 -0.720 -0.310
beta4_slope[16] -0.197 0.236 -0.662 -0.201 0.276
sigma_H[1] 0.205 0.054 0.110 0.202 0.322
sigma_H[2] 0.171 0.030 0.119 0.169 0.236
sigma_H[3] 0.195 0.044 0.114 0.193 0.287
sigma_H[4] 0.422 0.076 0.296 0.413 0.592
sigma_H[5] 0.999 0.208 0.626 0.987 1.436
sigma_H[6] 0.420 0.198 0.047 0.418 0.836
sigma_H[7] 0.299 0.060 0.207 0.291 0.439
sigma_H[8] 0.410 0.082 0.282 0.403 0.584
sigma_H[9] 0.525 0.129 0.326 0.507 0.816
sigma_H[10] 0.207 0.041 0.135 0.204 0.297
sigma_H[11] 0.278 0.047 0.204 0.272 0.381
sigma_H[12] 0.440 0.167 0.212 0.412 0.791
sigma_H[13] 0.214 0.038 0.152 0.211 0.298
sigma_H[14] 0.509 0.092 0.359 0.499 0.714
sigma_H[15] 0.247 0.041 0.178 0.243 0.341
sigma_H[16] 0.224 0.044 0.152 0.220 0.321
lambda_H[1] 3.055 4.055 0.148 1.732 14.424
lambda_H[2] 7.832 7.184 0.793 5.788 27.041
lambda_H[3] 6.107 9.122 0.241 3.106 31.593
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 3.428 7.210 0.044 1.066 21.984
lambda_H[6] 9.231 19.120 0.008 1.857 60.152
lambda_H[7] 0.015 0.010 0.003 0.012 0.040
lambda_H[8] 8.344 10.074 0.165 4.977 36.701
lambda_H[9] 0.015 0.010 0.003 0.012 0.040
lambda_H[10] 0.288 0.434 0.035 0.193 1.029
lambda_H[11] 0.265 0.424 0.012 0.122 1.301
lambda_H[12] 4.703 6.023 0.193 2.739 20.733
lambda_H[13] 3.592 3.215 0.293 2.732 11.978
lambda_H[14] 3.403 4.361 0.205 2.009 15.023
lambda_H[15] 0.026 0.037 0.003 0.017 0.105
lambda_H[16] 0.838 1.241 0.041 0.437 4.016
mu_lambda_H[1] 4.308 1.893 1.229 4.087 8.480
mu_lambda_H[2] 3.902 1.894 0.694 3.791 7.889
mu_lambda_H[3] 3.498 1.859 0.728 3.245 7.843
sigma_lambda_H[1] 8.564 4.289 2.028 7.870 17.966
sigma_lambda_H[2] 8.478 4.545 1.062 8.022 18.454
sigma_lambda_H[3] 6.279 3.980 0.995 5.455 16.088
beta_H[1,1] 6.895 1.067 4.291 7.064 8.536
beta_H[2,1] 9.872 0.508 8.770 9.901 10.795
beta_H[3,1] 8.005 0.773 6.127 8.109 9.225
beta_H[4,1] 9.078 7.888 -7.137 9.244 23.918
beta_H[5,1] 0.117 2.188 -4.323 0.261 3.856
beta_H[6,1] 3.248 3.895 -7.251 4.723 7.329
beta_H[7,1] 1.167 5.628 -11.029 1.742 11.295
beta_H[8,1] 1.238 2.944 -2.139 1.252 3.368
beta_H[9,1] 12.945 5.539 1.830 12.964 23.886
beta_H[10,1] 7.045 1.701 3.261 7.100 10.321
beta_H[11,1] 5.066 3.557 -3.033 5.800 9.905
beta_H[12,1] 2.629 1.094 0.747 2.541 5.003
beta_H[13,1] 9.078 0.881 7.165 9.156 10.507
beta_H[14,1] 2.187 1.112 0.217 2.179 4.259
beta_H[15,1] -5.992 3.853 -13.043 -6.303 2.496
beta_H[16,1] 3.560 2.649 -0.677 3.199 9.854
beta_H[1,2] 7.898 0.248 7.413 7.907 8.369
beta_H[2,2] 10.025 0.139 9.744 10.026 10.303
beta_H[3,2] 8.954 0.200 8.558 8.953 9.354
beta_H[4,2] 3.633 1.511 0.693 3.566 6.790
beta_H[5,2] 1.942 0.901 0.152 1.973 3.699
beta_H[6,2] 5.780 0.966 3.405 5.942 7.294
beta_H[7,2] 2.425 1.100 0.443 2.344 4.805
beta_H[8,2] 3.039 0.885 1.596 3.123 4.218
beta_H[9,2] 3.507 1.104 1.448 3.485 5.794
beta_H[10,2] 8.195 0.343 7.522 8.201 8.852
beta_H[11,2] 9.778 0.638 8.826 9.655 11.222
beta_H[12,2] 3.943 0.372 3.242 3.933 4.688
beta_H[13,2] 9.123 0.242 8.680 9.109 9.631
beta_H[14,2] 4.024 0.356 3.355 4.015 4.743
beta_H[15,2] 11.337 0.699 9.827 11.388 12.610
beta_H[16,2] 4.543 0.796 3.035 4.542 6.051
beta_H[1,3] 8.447 0.247 8.008 8.429 8.962
beta_H[2,3] 10.063 0.116 9.841 10.062 10.297
beta_H[3,3] 9.625 0.162 9.316 9.623 9.957
beta_H[4,3] -2.555 0.870 -4.324 -2.539 -0.932
beta_H[5,3] 3.837 0.605 2.575 3.844 4.979
beta_H[6,3] 7.838 1.138 6.320 7.461 10.380
beta_H[7,3] -2.519 0.738 -3.989 -2.503 -1.112
beta_H[8,3] 5.198 0.422 4.640 5.145 6.034
beta_H[9,3] -2.870 0.757 -4.391 -2.835 -1.439
beta_H[10,3] 8.704 0.269 8.187 8.708 9.247
beta_H[11,3] 8.533 0.288 7.903 8.558 9.028
beta_H[12,3] 5.244 0.326 4.447 5.284 5.749
beta_H[13,3] 8.840 0.175 8.487 8.846 9.175
beta_H[14,3] 5.717 0.282 5.080 5.740 6.192
beta_H[15,3] 10.375 0.321 9.755 10.370 10.997
beta_H[16,3] 6.228 0.614 4.875 6.281 7.262
beta_H[1,4] 8.245 0.187 7.845 8.259 8.582
beta_H[2,4] 10.123 0.123 9.860 10.129 10.351
beta_H[3,4] 10.125 0.163 9.769 10.136 10.409
beta_H[4,4] 11.813 0.439 10.943 11.816 12.672
beta_H[5,4] 5.463 0.711 4.299 5.381 7.090
beta_H[6,4] 7.098 0.893 4.974 7.383 8.255
beta_H[7,4] 8.165 0.348 7.466 8.175 8.849
beta_H[8,4] 6.699 0.225 6.287 6.703 7.109
beta_H[9,4] 7.187 0.474 6.236 7.188 8.123
beta_H[10,4] 7.730 0.224 7.312 7.724 8.195
beta_H[11,4] 9.387 0.196 9.015 9.391 9.770
beta_H[12,4] 7.138 0.216 6.720 7.130 7.607
beta_H[13,4] 9.046 0.138 8.770 9.049 9.307
beta_H[14,4] 7.741 0.223 7.312 7.741 8.196
beta_H[15,4] 9.464 0.234 9.013 9.463 9.921
beta_H[16,4] 9.349 0.243 8.897 9.339 9.862
beta_H[1,5] 8.979 0.142 8.684 8.982 9.254
beta_H[2,5] 10.781 0.092 10.600 10.781 10.968
beta_H[3,5] 10.929 0.168 10.620 10.922 11.278
beta_H[4,5] 8.388 0.458 7.506 8.384 9.303
beta_H[5,5] 5.443 0.555 4.172 5.490 6.411
beta_H[6,5] 8.783 0.620 7.909 8.627 10.291
beta_H[7,5] 6.806 0.332 6.174 6.807 7.474
beta_H[8,5] 8.210 0.196 7.869 8.201 8.598
beta_H[9,5] 8.207 0.487 7.231 8.212 9.206
beta_H[10,5] 10.106 0.223 9.655 10.111 10.535
beta_H[11,5] 11.504 0.228 11.036 11.505 11.964
beta_H[12,5] 8.483 0.201 8.106 8.479 8.893
beta_H[13,5] 10.010 0.126 9.773 10.005 10.267
beta_H[14,5] 9.206 0.238 8.772 9.195 9.712
beta_H[15,5] 11.163 0.247 10.670 11.171 11.633
beta_H[16,5] 9.918 0.184 9.529 9.925 10.259
beta_H[1,6] 10.189 0.192 9.863 10.173 10.626
beta_H[2,6] 11.515 0.110 11.300 11.512 11.731
beta_H[3,6] 10.811 0.159 10.458 10.823 11.087
beta_H[4,6] 12.877 0.818 11.264 12.904 14.486
beta_H[5,6] 5.882 0.600 4.728 5.864 7.047
beta_H[6,6] 8.821 0.679 7.043 8.949 9.779
beta_H[7,6] 9.798 0.551 8.747 9.796 10.917
beta_H[8,6] 9.529 0.263 9.076 9.535 9.986
beta_H[9,6] 8.448 0.805 6.882 8.440 10.063
beta_H[10,6] 9.520 0.312 8.847 9.546 10.063
beta_H[11,6] 10.814 0.354 10.069 10.842 11.421
beta_H[12,6] 9.377 0.255 8.908 9.357 9.920
beta_H[13,6] 11.041 0.156 10.750 11.034 11.358
beta_H[14,6] 9.828 0.299 9.253 9.829 10.401
beta_H[15,6] 10.849 0.436 10.005 10.856 11.686
beta_H[16,6] 10.536 0.239 9.995 10.546 10.987
beta_H[1,7] 10.886 0.879 8.605 10.994 12.295
beta_H[2,7] 12.201 0.443 11.311 12.210 13.040
beta_H[3,7] 10.536 0.659 9.067 10.595 11.621
beta_H[4,7] 2.521 4.251 -5.576 2.499 11.163
beta_H[5,7] 6.395 1.779 3.021 6.338 10.549
beta_H[6,7] 9.666 2.445 5.081 9.585 16.011
beta_H[7,7] 10.727 2.795 5.179 10.703 16.159
beta_H[8,7] 10.934 0.994 9.386 10.908 12.414
beta_H[9,7] 4.490 4.181 -3.874 4.492 12.709
beta_H[10,7] 9.852 1.450 7.197 9.762 12.968
beta_H[11,7] 10.989 1.723 7.928 10.876 14.711
beta_H[12,7] 9.984 0.948 7.854 10.081 11.506
beta_H[13,7] 11.674 0.722 9.990 11.746 12.859
beta_H[14,7] 10.424 0.981 8.401 10.474 12.195
beta_H[15,7] 11.947 2.260 7.619 11.896 16.419
beta_H[16,7] 12.322 1.284 10.223 12.134 15.245
beta0_H[1] 8.632 13.980 -20.008 8.700 35.237
beta0_H[2] 10.665 6.619 -2.022 10.566 23.798
beta0_H[3] 10.372 9.934 -9.744 10.210 30.975
beta0_H[4] -0.519 185.952 -389.870 -3.617 374.282
beta0_H[5] 3.843 21.866 -40.385 4.247 47.333
beta0_H[6] 7.060 47.633 -100.852 7.647 110.297
beta0_H[7] 5.945 129.145 -266.921 6.003 265.114
beta0_H[8] 6.095 15.949 -13.271 6.570 25.120
beta0_H[9] 5.170 123.763 -244.656 3.369 254.814
beta0_H[10] 9.965 32.752 -55.359 9.368 82.656
beta0_H[11] 8.698 50.022 -105.075 9.568 107.144
beta0_H[12] 6.837 11.952 -15.289 6.797 28.624
beta0_H[13] 9.761 10.531 -10.902 9.961 30.264
beta0_H[14] 7.271 12.267 -16.761 7.016 32.104
beta0_H[15] 10.667 107.451 -207.728 8.847 231.976
beta0_H[16] 8.666 25.178 -45.260 8.417 64.634